Cervical intervertebral prostheses are known (EP-A-1 344 508) having two cover plates which are to be connected to the end plates of the adjacent vertebral bodies and between which there is a sliding core which allows the cover plates a relative movement intended to simulate the articulated mobility of the intervertebral disk that has been replaced. To secure the cover plates in their intended position between the vertebral bodies, the cover plates in the known prosthesis are connected to securing plates which extend from the ventral edge of the cover plates, perpendicularly thereto, and are screwed to the ventral surface of the associated vertebral body. The ventral surfaces of the vertebral bodies on which the securing plates come to lie do not always extend exactly perpendicular with respect to the end plates of the vertebral bodies on which the main surfaces of the cover plates come to lie. This prevents the securing plates from bearing across their entire surface on the vertebral bodies, and it impairs the stability of the cover plates.